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Testing Stock Market

Efficiency Using Risk-Return Parity Rule

N P Srinivasan and M S Narasimhan

Although the concepts of efficiency have been extensively researched, an efficientstock market has remained elusive. Thesubject is of particular concern in India now because of the increasing dependence onthe capital market for financing industrialgrowth.

S K Barua and V Raghunathan pre-sented two articles in Vikalpa (July-September 1986 and July-September 1987)arguing that the Indian capital market wasinefficient. Using Reliance share prices,they tried to demonstrate that schemesyielding returns unrelated to risk existed.

Srinivasan and Narasimhan in this arti-cle question the methodology used byBarua and Raghunathan and elaborate onthe concepts of risk-return parity and effi-ciency, drawing a distinction between infor-mation efficiency and market efficiency.

TV P Srinivasan is IFCI Chair Professor and M S Narasimhan is Research Scholar at the Department of Commerce, University of Madras.

An efficient capital market is indispensable for creating investors' confidence and for a proper al-location of capital among enterprises and sectors.

Is the Indian capital market efficient? Two dif-ferent views have appeared in recent issues of

Vikalpa.

Barua and Raghunathan argued in their arti-cle, 'Inefficiency of the Indian Capital Market,'(Vikalpa, July-September 1986), that the Indiancapital market was inefficient. Using the Relianceexample, hypothetical values, and applying therisk-return parity rule, they concluded that themarket was inefficient. The market was unable tomaintain risk-return parity.

Ramesh Gupta in his rejoinder, 'Is the IndianCapital Market Inefficient or Excessively Specula-tive?' (Vikalpa, April-June 1987) explained cer-tain peculiarities of the Indian capital market andconcluded that the violation of the risk-return par-ity might be due to excessive speculation and notdue to the inefficiency of the market. Barua andRaghunathan in a second article,'Inefficiency andSpeculation in the Indian Capital Market,' (Vik-alpa, July-September 1967), re-examined their hypothesis using real data on the Reliance issuewhich was available by then and held that their earlier conclusion remained valid. They held thatthe peculiarities of Indian capital market pointedout by Ramesh Gupta did not affect their conclusion.

Barua and Raghunathan's articles suffer froma misunderstanding about the concepts of marketefficiency and risk-return parity. Their methodo-logy is questionable. We have attempted below to:

• clarify the concepts of market efficiency

and risk-return parity rule and explainthe relationship between them

• show the inadequacy in the methodology

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for evaluating market efficiency used byBarua and Raghunathan

• propose a framework for evaluating marketefficiency using the risk-return parity rule.

Market Efficiency and Risk-Return ParityRule

Capital market efficiency implies that informationis widely and cheaply available to investors andthat all relevant and ascertainable information isfully reflected in security prices.

There are three forms of capital market efficiency:

• weak form, in which security prices

impound all historical prices

• semi-strong form, in which security prices

impound all publicly available informa-

tion • strong form, in which security prices

impound all public and private (inside)information.

The strong form of market efficiency does not seem possible. A number of empirical studies have foundthat markets can only achieve the semi-strong formof efficiency and therefore, the weak form also.

The semi-strong form of market efficiency implies that most investors cannot devise tradingschemes based on publicly available information to

earn excess (or abnormal) rates of return—returnsabove the level available to any investor bearingthe same risk. It should be noted that under thesemi-strong form of capital market efficiency, aninvestor with private or inside information canachieve an excess return.

Barua and Raghunathan have viewed marketefficiency as its ability to maintain risk-return par-ity at all times through its pricing mechanism. Their view implies that a higher risk taken should actu-ally be rewarded with higher return, commensuratewith the risk assumed. This need not be so. For,risk is the exposure to a chance of injury or loss and

not to actual or certain loss. Hence, the ex-post re-turn may be much less or even be a loss comparedwith ex-ante expected return. A violation of therisk-return parity rule in the ex-post sense cannot be interpreted as sure evidence of market ineffi-ciency. On the other hand, any evidence of abnor-mal return would indicate inefficiency only if therisk-return parity holds ex-ante.

Information Inefficiency

Empirical evidence in Western countries alsoshows that while over the long run there is the expected positive sign and relationship between risk and return, the shorter-term relationship betweenrisk and return has been erratic. The shorter-term

findings have not been explained satisfactorily.Furthermore, there is enough evidence ineconomic literature that markets are information-ally inefficient. The implication is that informa-tional inefficiency cannot be conclusive proof of capital market inefficiency. Evidence of abnormalreturns can be due to informational inefficiency,not necessarily market inefficiency.

Barua and Raghunathan's approach of evaluating market efficiency on an ex post-facto basis canlead to wrong conclusions about market efficiency.To appreciate the issues, it may be useful con

sider the following two examples.

Example 1: Investors A, B and C are offeredinterest-free loans of Rs 1 lakh each subject to thefollowing two conditions:

i) The loan is to be repaid after one year,

and

ii) Each should invest either in :

a) government securities or bank deposits,or

b) one or more of 12 shares, all of which belong to a similar risk class.

All the three investors are risk-takers andhence prefer to invest in shares. Investor A, on the basis of some analysis of his own, chooses investin the first six securities on the list. Investor B, in-vests in the last six securities on the list. Investor Cselects three shares from the first six securities andthree from the last six securities.

During the year, prices of the first six sec-urities went up by 75 per cent whereas prices of thelast six securities fell by 75 per cent. The reason for such wide variations can be due to peculiar inci-

dents during the year, beyond our ability toforecast.

Investor A will have a 75 per cent returnwhereas investor B will suffer a loss of 75 per cent.Investor C will neither gain nor lose. Although allof them took similar risks, their actual returns var-ied widely. How do we use the risk-return parityrule to judge efficiency? Investor A can acclaim

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that the market is efficient, but B will cry that themarket is inefficient while C can conclude that it iserratic. Who is correct?

Example 2: Companies A and B, whose currentshare prices are Rs 12 (face value Rs 10), offer convertible debentures on a rights basis in the ratio

of 10 debentures of Rs 100 each for every 100shares. Each debenture will be converted into 10shares of Rs 10 each at par at the end of first year.Investors X and Y, each of whom holds 100 sharesof each company, apply for 10 debentures each.

There is a 50 per cent chance that the year-endmarket price of Company A's shares would beRs. There is a similar chance for Company B'sshare prices. Let us assume that the correlation between share price movements of Company Aand Company B shares is very weak (neither positive nor negative) and hence, por tfoliotheory cannot be to reduce the risk.

Both investors decide to sell their rights after conversion. Investor X decides to sell security A ona cash basis at the end of the year but pre-sells sec-urity B on the forward market to avoid a fall in its price. Investor Y decides to sell security B on acash basis at the end of the year but pre-sells secur-ity A on the forward market. Each avoided the price fluctuations in one security while taking therisk OB the other. Their risks were equal.

The year-end price of security A is Rs 15 andof security B is Rs 5. X gained Rs 5 (Rs 15 - Rs 10)

from security A and was not affected by the fall in prices of security B. On the other hand, Y did notgain by the increase in the price of security of A (ashe had already pre-sold it) but suffered a loss fromsecurity B. If X claims that the market is efficientthen Y cannot. How do we interpret suchconclusions ?

An outside investment analyst can rightly point out that it is not a question of market effi-ciency but of individual investor efficiency. In-vestor X was luckier than investor Y. An ex-postfacto analysis based on one or two securities is nota valid approach to test market efficiency.

Inadequacies in Methodology:

In their hypothetical example in the July-September 1986 article, Barua and Raghunathan

concluded that the, market was inefficient as risk-return parity had not been maintained for most of the assumed values of one security. There are cer-tain inadequacies in their methodology which wediscuss below:

Whenever a company announces a rights issue,

there may be an increase in price for the followingtwo reasons:

i) The existing investor who has shares 'withrights' can expect to enjoy the gain fromsuch rights issue if he continues to holdthe shares and exercises his rights.

ii) There could be an expectation of addi-tional growth in the company's incomei.e. EPS (Earning Per Share), as the ad-ditional amount raised through rightsare normally used in profitableventures.

There was an expectation of growth in the caseof Reliance, the example used by Barua andRaghunathan. When the company announced itsrights issue for a huge amount of Rs 400 crore, ithad profitable ventures on hand. There was reasonto expect that its Earnings Per Share (EPS) wouldgrow several-fold with the completion of those pro- jects. Given such a situation, calculating the ex-rights price by adjusting for reason (i) above alonemay not be correct. In other words, if Rs 230 is the pre-announcement price and if the company has no profitable venture at the time of rights announce-ment the cum-rights price of Rs 272 may be re-

duced to the previous level of Rs 230. As this con-dition is not true, it is not correct to expect that theex-rights price should be around Rs 230.1 In addi-tion, one has to consider the share premium thatwould be added to the net worth after conversion.The book value per share would then increase fromRs 59.16 before the rights issue to Rs 84.36 after conversion. This would also influence an increasein the share price after conversion.

Unclear Assumptions

Apart from an ex-rights price of Rs 230, Barua andRaghunathan's conclusion is based on two other grounds:

1In fact, when the Reliance rights issue opened in December '86 its share price was around Rs 212. It moved up continu-ously to Rs 270 before the budget announcement in February1987. Subsequently, many abnormal things forced the priceto fall to Rs 120 by mid 1987.

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i) The ex-rights price of share wouldcontinue to be Rs 230 throughout the period from 15.9.86 to 15.9.87.

ii) When there is an indication that the price of the share is going to be lower than the current market price, it is better for an investor to sell in the forwardmarket at Rs 272 and gain by closing thedeal at a lower price2.

They assume that by selling in a forward con-tract at Rs 230, an investor will gain 20 per centinterest (short term lending rate) for almost 11months by continuously carrying forward the trans-action. But a purchaser E will carry forward and pay interest only if two conditions are satisfied:

i) he expects that prices of the share willincrease in future, and

ii) the rate of increase in price will at least be equal to the interest rate.

When these conditions are not fulfilled E willsquare up the contract and stop interest payment.In other words, the purchaser also takes a risk bycarrying forward the contract. If the future is as expected, both investors C and E will gain whereasinvestor D will not. Vice versa, C and E will suffer when D gains. Investors C and E, who took a risk,have an opportunity to get a higher reward than D.This opportunity to get a premium for a higher risk is risk-return parity and not actual or certain pre-mium for higher risk.

In their computation of the holding of in-vestors C and D, Barua and Raghunathan have as-sumed that both will apply for the additional 25 per cent above their eligible rights quotas. They fail toconsider the same when calculating the ex-rights price. Even by the crude method, the ex-rights price after such an adjustment for the additionalsubscription would be Rs 204.

Inadequacy in Real Example

Barua and Raghunathan in their second article(Vikalpa, July-September 1987) used real datawhich were then available and showed how the

It is not clear how an investor can enter the forward contractwithout risk at the cum-rights price of Rs 272 with ex-rightsholdings. Perhaps, this is an error. The rectification of thisalone would neither affect their conclusion nor support our argument.

market still violated the risk-return parity. Their calculations using the real example also suffer fromsimilar limitations which are explained below.

In their example, both investors C and D ap- plied for debentures on 1.12.86 and sold them on1.5.87. Investor D in addition, sells two equity

shares on a forward basis on 1-12-86 and carriesforward the transaction till 30.4.87. Barua andRaghunathan show that the return to investor C is38 per cent for five months while that to investor Dis 104 per cent. Their argument is that as both in-vestors C and D purchased and sold debentures onthe same date, the additional gain to Investor D isderived solely from carrying the transaction for-ward. Here Barua and Raghunathan assume that Dwill carry forward the transaction for exactly fivemonths. They provide no explanation or reason.

Alternative Termination Periods

Sale of debentures and the termination of carryforward transaction are two separate and indepen-dent decisions. Investor D could have .terminatedthe contract at any time depending on his position.For example, seeing a continuous rise in price inthe initial few periods (during that period when hehad to pay a large sum to buyers) investor D couldhave squared out the contract, if he expected afurther rise in prices. Table 1 below gives the cashinflow/cash outflow to investor D for varioustermination periods:

Table 1: Cash Flow in Rupees to Investor D for

various Termination Dates

* Based on amount paid/received on account of the price differ-ence and carry forward charges till the termination date. A sumof Rs 55, being the price difference on sale of debentures (Rs 200- Rs 145) is to be added to both C and D.

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The cash inflow to C is zero for all periods as he hasnot entered into a forward transaction. But D's cashinflow varies depending on the termination date andruling price on that date.

If we apply the risk-return parity rule as in-terpreted by Barua and Raghunathan, the market isefficient till 23.3.87 but suddenly becomes ineffi-

cient from 3.4.87. The full impact of inefficiencywas felt on 30.4.87 when the risk-return parity wasseriously affected. To arrest such inefficiency, themarket price should move up.

Wisdom of Market

But an important incident that took place between16.4.87 and 30.4.87 should be considered. At Re-liance's annual general meeting on 29.4.87, it wasconfirmed that the results of the company for theyear ending 31.12.86 were poor. The dividend was

slashed from 50 per cent in the previous year to 25 per cent for 198"6. Reliance share price which wasruling around Rs 190 dropped to Rs 140 on 29.4.87and further to Rs 127 on 4.5.87. Barua andRaghunathan indirectly argue that in order to protectrisk-return return parity, the market should ignorethese facts.1 But, if the market ignored these factsthen it would make a good case for its "own ineffi-ciency. Wisely, the market did not ignore availableinformation.

The termination dates in our analysis (Table 1)may be objected on to the ground that a forwardcontract should be compared with a cash transactionand not with 'no transaction'. To take care of suchobjections, the 'example can be modified as follows.

Modified Example

Investors C and D have two shares and, in addition,they apply for one debenture. Investor C is tradingon a cash basis and investor D on the forwardmarket. As D has two shares on hand and expectstwo additional shares on conversion, he could enter the forward market for four shares. Now let us as-sume, that at each termination period, C sells twoshares on cash and D delivers two shares and

squares out his obligation on the remaining twoshares. This situation enables us to maintain anequal status between investors C and D.

1Interestingly in their first article, they made a specific sugges-tion like adjustment in Debenture 'F' series price and share

prices to maintain risk-return parity but fail to make any sug-gestion this time. To our knowledge this is the only alternativefor maintaining risk-return parity.

The results comparing forward with cash trans-

action (Table 2) and with "ho transaction (Table 1)are similar. Our discussion and conclusion basedon Table 1 remain valid.

Ex Post facto Analysis Invalid

Another disturbing statement in Barua andRaghunathan's second article (Vikalpa, July-September, 1987) is as follows:

"The market could not maintain the risk-return parity. It is inefficient. This statementassumes that the actual drop in price of Re-liance share is in line with the expectation of

the market."

The exact meaning of their assumption is notclear. If it means that the fall in Reliance share price to Rs 130 was already expected, investor Ccould have sold his two shares between 12.12.86and 29.1.87 to get the maximum gain and also soldthe debenture for Rs 270 in an unofficial deal. No buyer would carry forward the transaction if thefall in price was strongly expected. There isanother way of interpreting this statement. The fallin price is due to genuine demand and supply, based on market information, and is not artificially

created. If so, their statement really endorsesmarket efficiency.

Barua and Raghunathan's analysis of marketefficiency suffers from two errors:

i) They have used ex-post facto analysis for evaluating risk-return parity and marketefficiency. As already discussed, ex-postfacto analysis is invalid.

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